Decoding of codes on Picard curves

Abstract

The Picard curves are genus three curves with a non trivial automorphism, which have been intensively studied due their connection with interesting number theoretic problems. In 1989, R. Pellikaan obtained an algorithm decoding geometric codes up to [(d*-1)/2]-errors, where d* is the designed distance of the code. His algorithm is not completely effective, but recently some authors have given an effective answer to Pellikaan's algorithm using the particular features of special curves, such as the Klein quartic and the hyperelliptic curves. In this paper we show that the Picard curves are suitable to obtain an effective answer to Pellikaan's algorithm.